Is strategy B better
Over 60 independent days, strategy A has an average daily return of 10 and strategy B of 11 (in the same units). Both have a daily standard deviation of 2, and the two samples are independent.
Find the two-sample t-statistic for the difference in means:
Fractions, decimals with at least 3 significant digits, and expressions such as sqrt(2)/2, e^-1 or pi/4.
Each sample mean has variance .
Variances of independent quantities add.
h
s Shown after a correct answer. Revealing it first marks the problem as seen, not solved.
Idea. The difference of two independent sample means has a variance equal to the sum of their variances. The t-statistic is the observed difference divided by its standard error.
Step 1: standard error.
Step 2.
So the difference is significant at the 5% level (two-sided), with 118 degrees of freedom.
The caveat. The two strategies probably trade the same market on the same days, so their returns are not independent. With positively correlated returns, the right test uses the daily differences (a paired test), whose standard deviation can be much smaller, and the t-statistic much larger.